MNRAS 492, 3803–3815 (2020) doi:10.1093/mnras/staa049 Advance Access publication 2020 January 10 Standard siren speeds: improving velocities in gravitational-wave measurements of H0 Cullan Howlett ‹ and Tamara M. Davis School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072, Australia Downloaded from https://academic.oup.com/mnras/article-abstract/492/3/3803/5700291 by University of Queensland user on 20 April 2020 Accepted 2020 January 6. Received 2020 January 6; in original form 2019 August 30 ABSTRACT We re-analyse data from the gravitational-wave event GW170817 and its host galaxy NGC 4993 to demonstrate the importance of accurate total and peculiar velocities when measuring the Hubble constant using this nearby standard siren. We show that a number of reasonable choices can be made to estimate the velocities for this event, but that systematic differences remain between these measurements depending on the data used. This leads to significant changes in the Hubble constant inferred from GW170817. We present Bayesian model aver- = +13.4 −1 −1 aging as one way to account for these differences, and obtain H0 66.8−9.2 km s Mpc . Adding additional information on the viewing angle from high-resolution imaging of the radio = +7.3 −1 −1 counterpart refines this to H0 64.8−7.2 km s Mpc . During this analysis, we also present an alternative Bayesian model for the posterior on H0 from standard sirens that works more closely with observed quantities from redshift and peculiar velocity surveys. Our results more accurately capture the true uncertainty on the total and peculiar velocities of NGC 4993 and show that exploring how well different data sets characterize galaxy groups and the velocity field in the local Universe could improve this measurement further. These considerations impact any low-redshift distance measurement, and the improvements we suggest here can also be applied to standard candles like Type Ia supernovae. GW170817 is particularly sensitive to peculiar velocity uncertainties because it is so close. For future standard siren measurements, the importance of this error will decrease as (i) we will measure more distant standard sirens and (ii) the random direction of peculiar velocities will average out with more detections. Key words: methods: statistical – galaxies: distances and redshifts – galaxies: individual: NGC 4993 – cosmological parameters. constant, H , analogous to methods using ‘standard candles’ (Type 1 INTRODUCTION 0 Ia supernovae – SNe Ia; Cepheid variable stars, etc.) and ‘standard On 2017 August 17, the Advanced LIGO (LIGO Scientific Collab- rulers’ (e.g. Baryon Acoustic Oscillations – BAOs; the cosmic oration 2015) and Advanced Virgo (Acernese et al. 2015) detectors microwave background – CMB). This determination of the Hubble observed gravitational waves originating from event GW170817. constant was made possible through the combination of cosmo- Modelling of this signal later identified this event as a result of the logical luminosity distance inferred from the gravitational-wave merger of two compact neutron stars (Abbott et al. 2017a, 2019). In signal, combined with the observed total and peculiar velocities of the short time after that, electromagnetic counterparts were detected NGC 4993. The luminosity distance inferred from the gravitational across a number of wavelengths (Abbott et al. 2017c) resulting in wave is consistent with independent measurements of the distance the first multimessenger detection of a gravitational wave. to NGC 4993 (e.g. Hjorth et al. 2017;Imetal.2017; Cantiello The presence of the electromagnetic counterparts gave a pre- et al. 2018). It is worth noting that in cosmological terms, standard cise determination (with probability of chance association P< sirens and candles are very similar; both measure the luminosity 0.004 per cent; Abbott et al. 2017b) that the host of the grav- distance through calibration of an astrophysical signal, which in itational wave was NGC 4993, a low-redshift lenticular galaxy. the case of standard sirens is the frequency and rate of change The combination of gravitational wave and host identification then of frequency of the gravitational wave. This can be compared to allowed for the first ever ‘standard siren’ measurement of the Hubble standard rulers, which measure a different cosmological quantity, the angular diameter distance. The Hubble constant is one of the fundamental constants de- scribing our cosmological model. It describes how fast the Universe E-mail: [email protected] C 2020 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society 3804 C. Howlett and T. M. Davis is expanding, and how fast objects are receding from each other. no peculiar velocity and were comoving observers (in the CMB = − Sun Precise determination of this constant has been one of the foremost frame) using the approximation zcmb zobs zp and then the goals of cosmology since its discovery, with the majority of Hubble constant is inferred using measurements using either standard candles or standard rulers. In = obj + approx + recent years, tensions have arisen between measurements from these czcmb vp H0 dL/(1 zcmb). (3) two methods. Results from a combination of Planck CMB and var- −1 −1 ious BAO measurements prefer H0 = 67.66 ± 0.42 km s Mpc However, we will tacitly avoid such approximations in this work and (Planck Collaboration VI 2018); however, this requires assuming demonstrate that they are unnecessary (and inadequate) for inferring a lambda cold dark matter (CDM) cosmological model to ex- the Hubble constant from standard sirens. It is also common to use Downloaded from https://academic.oup.com/mnras/article-abstract/492/3/3803/5700291 by University of Queensland user on 20 April 2020 trapolate the constraints from high redshift. Results using the local redshifts and velocities interchangeably, which leads to potential distance ladder (SNe anchored using Cepheids and local geometric confusion/mistakes. For clarity, we provide in Table 1 a list of −1 −1 distances) prefer H0 = 74.03 ± 1.42 km s Mpc (Riess et al. definitions for the various terms used in this work. 2019).1 The tension between these two is currently at the level Regardless of the approximations used, constraining the Hubble of ∼4.5σ and hints at the presence of unknown systematics or new constant using gravitational waves (or indeed any local distance fundamental physics. It seems unlikely that this will be resolved over measurement) requires knowledge of the observed object’s total the coming years without additional, independent measurements. and peculiar velocities. There are a number of methods to estimate Standard sirens using gravitational waves present the exciting these in combination. First, the total velocity of the host can be prospect of such a measurement, and may identify a way to resolve measured spectroscopically and combined with a measurement of the current tension. the peculiar velocity of the host. However, in this case, the total and Standard sirens are one of the cleanest distance measurements peculiar velocities of the host galaxy are influenced by its motion available, but they are not without their own sources of uncertainty, within its Local Group or cluster, which includes non-linear effects both statistical and systematic. Especially in the infancy of this from growth of structure and/or virialized motions that may be technique, with few measurements available, these could cause hard to account for in the peculiar velocity estimate. The peculiar biases in the recovered constraints on the Hubble constant. The velocity for a single object is also subject to considerable statistical potential source of systematic uncertainty we concentrate on in error. It is often preferable, as was done in Abbott et al. (2017b), to this paper is the influence of peculiar velocities. Peculiar velocities use instead the total and peculiar velocity of the group to which the have long been known to potentially bias measurements of H0, object belongs such that non-linear motions are ‘smoothed-out’ and particularly if the sources are nearby (e.g. Dressler et al. 1987; the uncertainty in the peculiar velocity reduced. In this case, there Sandage & Tammann 1990; Tonry et al. 2000; Tully et al. 2008). We still remains a choice of how to compute which galaxies belong to begin by summarizing how peculiar velocities impact H0 estimates the same group as the host, and how to obtain the peculiar velocity in general, and then consider the specifics of the peculiar velocity of the group. estimates of GW170817’s host, NGC 4993. In terms of estimating the group peculiar velocity, there are two With determination of the host galaxy and a measurement of the approaches commonly adopted. The first is to use a ‘peculiar veloc- luminosity distance dL, we can infer the Hubble constant via ity survey’; a catalogue of measured peculiar velocities estimated for objects with secondary distance measurements (more detail + = + + obj + Sun (1 zobs) (1 z¯(dL,H0,zobs)) 1 zp 1 zp , (1) on these is given in Section 3). Different interpolation methods can then be applied to this catalogue to estimate the peculiar obj where zobs is the observed redshift and zp is the peculiar redshift velocity at the location of the group. In this case, however, it that arises from the peculiar velocity of the observed object. is worth noting that peculiar velocity is not actually the directly z¯(dL,H0,zobs) is the cosmological redshift of the object, which can observed quantity from peculiar velocity surveys (it is the change be computed given a choice of the Hubble constant and an inference in magnitude or size caused by the underlying peculiar velocity) Sun of the luminosity distance. zp is an additional redshift arising from and hence the uncertainties in the measured peculiar velocities are our Sun’s motion with respect to the comoving frame, typically not typically Gaussian distributed (unless an approximate estimator calculated using the CMB dipole.